论文标题
$ \ mathbb {z} $ - 边界链接的属
The $\mathbb{Z}$-genus of boundary links
论文作者
论文摘要
$ \ mathbb {z} $ - $ s^3 $中的$ l $的属是本地平坦的，嵌入式，连接的表面的最低属，其边界为$ l $，与补充无限循环的基本组。我们表征了$ \ mathbb {z} $ - 边界链接的属，其单个变量blanchfield表单，我们提供了一些应用程序。特别是，我们表明了一个结的奶昔属的变体，即$ \ mathbb {z} $ - 摇属属，等于结的$ \ mathbb {z} $ - 结的属。
The $\mathbb{Z}$-genus of a link $L$ in $S^3$ is the minimal genus of a locally flat, embedded, connected surface in $D^4$ whose boundary is $L$ and with the fundamental group of the complement infinite cyclic. We characterise the $\mathbb{Z}$-genus of boundary links in terms of their single variable Blanchfield forms, and we present some applications. In particular, we show that a variant of the shake genus of a knot, the $\mathbb{Z}$-shake genus, equals the $\mathbb{Z}$-genus of the knot.
